Tag: Mathematical connections

On Friday I met with Simon and my head of department Pete to try and create an initial framework of topics for the scheme of work. The target was to have a loose order of topics to cover the first year of an AS course, changing from our previous structure of 3 teachers each teaching individual modules, to a linear structure that will probably be taught by two teachers.

One of the real benefits of moving to the linear scheme will be how much time it frees up compared to our old structure by removing some of the assessment. Previously we have tested students each half term in all three modules. This has been in the form of a one hour assessment based on past exam questions, starting off quite narrow and expanding as more content has been covered. By the time these assessments had been completed and feedback given we were looking at 6 hours of teaching time lost per half term. In a linear system I would anticipate that the assessment could be reduced to a single one hour paper initially, allowing us at least 4 hours more time each half term.

Using the AS topic headings from the freely available MEI SoW we began to organise the topics into a coherent order, focussing on pre-requisite knowledge, and links between topics.

Having a hard copy of the MEI SoW to hand (http://mei.org.uk/2017-sow) was useful as we moved topics around. It is designed to be editable for any specification and allowed us to focus on the connections between mathematics topics

One of the striking things that came up in the conversation was how we had previously compartmentalised topics. Surds and Indices is a C1 topic, whereas Logarithms and Exponentials is a C2 topic. Yet they are different ways of looking at the same thing and surely if taught together would allow a much better understanding of where logarithms come from, something that I have always struggled to get students to see. As such we have decided that the first thing we will teach is logarithms and exponentials, while at the same time revising the surds and indices materials students should have met at GCSE. This means that students will be meeting something new straight away, hopefully catching interest, but also brings in a link to previous learning.

A provisional model is shown in the diagram below, pure units in green, statistics in blue and mechanics in orange.

The model we have come up with looks very heavily weighted to the first half term. However of the five pure elements, four should be revision from GCSE. Historically we have taught these as the first half term of C1, a third of our teaching time across the whole course. While thinking about the links in topic areas we discussed how some of the topics (see the right-hand columns of the grid above) might be better spread over the course, with pieces put into different topics to improve connections. An example would be that for transformation of graphs in the past we have taught completing the square early in the course and touched back to how this links to transformations much later. We feel that by expecting to make links with transformations at appropriate points throughout the course as it naturally arises the links should be much clearer and stronger for the students.

Coordinate geometry is another topic that we felt was better split across the year. Tangents and normal will fit in as an introduction to differentiation and circles has strong links to trigonometry.

With the statistics elements of the courses we decided that the large data set should be introduced as early as possible. This meant that we inserted data collection, which is largely about sampling, into the first block of topics. This also got me thinking – I had previously decided that I would not make the decision on which exam board to use until much later. However in order to introduce the large data set I need to have made the decision so that students are used to working with the relevant data.

Mechanics fits in very well with elements of the ‘pure’ maths, particularly with calculus and variable acceleration. This has always been something that I have felt is a missed opportunity in the teaching of A-level maths, it should create a connection and allows us to show the roots of these skills in a real life situations.

This of course is only a first attempt and will continue to evolve as we move forward. At our next meeting with Simon we are going to look at the individual content statements for each topic and to order those, whether within the current structure or moved to further emphasise links.